Exponential stabilization of fixed and random time impulsive delay differential system with applications

A. Vinodkumar; T. Senthilkumar; S. Hariharan; J. Alzabut; A. Vinodkumar; T. Senthilkumar; S. Hariharan; J. Alzabut

doi:10.3934/mbe.2021121

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 3: 2384-2400. doi: 10.3934/mbe.2021121

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Exponential stabilization of fixed and random time impulsive delay differential system with applications

1.
Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641112, India
2.
Department of Mathematics, Amrita School of Arts & Science, Amrita Vishwa Vidyapeetham, Kochi, Kerala 682024, India
3.
Department of Mathematics, D G Vaishnav College, Chennai, India
4.
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Received: 21 January 2021 Accepted: 25 February 2021 Published: 10 March 2021

In this work, we study the problem of $ p- $th moment global exponential stability for functional differential equations and scalar chaotic delayed equations under random impulsive effects. Meanwhile, the $ p- $th moment global exponential synchronization for the proposed equations is also discussed, whereas the main results are proved by using Lyapunov function and Razumikhin technique. Furthermore, the impact of fixed and random time impulses are presented by applying the results to Mackey Glass blood cell production model and Ikeda bistable resonator model. Finally, the effectiveness of fixed and random impulses are depicted via graphical representations.
- random impulses,
- Lyapunov function,
- Razumikhin technique,
- global exponential stability,
- delay differential equations
Citation: A. Vinodkumar, T. Senthilkumar, S. Hariharan, J. Alzabut. Exponential stabilization of fixed and random time impulsive delay differential system with applications[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2384-2400. doi: 10.3934/mbe.2021121

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Abstract

In this work, we study the problem of $ p- $th moment global exponential stability for functional differential equations and scalar chaotic delayed equations under random impulsive effects. Meanwhile, the $ p- $th moment global exponential synchronization for the proposed equations is also discussed, whereas the main results are proved by using Lyapunov function and Razumikhin technique. Furthermore, the impact of fixed and random time impulses are presented by applying the results to Mackey Glass blood cell production model and Ikeda bistable resonator model. Finally, the effectiveness of fixed and random impulses are depicted via graphical representations.

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